Silvan Widmer gave the Swiss an early lead, but Giovanni Di Lorenzo equalised - and in the 90th minute, VAR intervened as Italy were awarded a penalty.
But Jorginho blazed over the bar, meaning both teams have 15 points going into their respective final group game, with Italy travelling to Northern Ireland and Switzerland at home to Bulgaria on Monday.
Schär, whose last Newcastle appearance came back in August, picked up a yellow card in Friday's match.
In the same group, Northern Ireland beat Lithuania 1-0 in Belfast, with Benas Satkus' own goal proving decisive. Jamal Lewis replaced former Magpies man Shane Ferguson in the 70th minute.
At under-21 level, Elliot Anderson will have to wait for his Scotland bow as he was an unused substitute in a 2-1 win over Kazakhstan in Dundee, while Oisín McEntee wasn't involved in the Republic of Ireland's 2-0 defeat to Italy.